Volume 25, Issue 2 - Special Issue: Fuzziness and Applied Soft Computing

The examinee and the examiner play pivotal roles in the educational grading system. Students’ academic performance evaluation by multiple experts involves epistemic uncertainty, which can be modeled using a fuzzy set theory. How many evaluators/experts are almost similar in their perceptual subjective evaluation of the students answer paper? In other words, how many experts are reliable for a particular evaluation task with a defined possibility level? In this paper, the focus is on object’s features ( students’ marks ) as a basis in the subjective evaluation process to identify the degree of similarity among the domain experts. The case study reveals that 11 out of 20 evaluators are similar in their decision making of students’ academic performance with possibility ( α -level cut, 0.98). The inter-rater reliability ( κ -coefficient) among the selected 11 teachers is 0.41, which signifies a fair/moderate agreement in the evaluation process. This paper proposes an approach that is useful for the selection of experts having similar perceptions in judgment. This paper demonstrates a case study showing how it is useful to educational policy makers in the selection of examiners.

The aim of this article is to develop a representation theory of interval-valued Łukasiewicz–Moisil algebras; the concept of interval fuzzy sets involves the role that the notion of field of sets plays for the representation of Boolean algebras. This theory provides both a semantic interpretation of a Łukasiewicz interval-valued logic and a logical basis for the interval fuzzy sets theory.

The electric wheelchair gives more autonomy and facilitates movement for handicapped persons in the home or in a hospital. Among the problems faced by these persons are collision with obstacles, the doorway, the navigation in a hallway, and reaching the desired place. These problems are due to the difficult manipulation of an electric wheelchair, especially for persons with severe disabilities. Hence, we tried to add more functionality to the standard wheelchair in order to increase movement range, security, environment access, and comfort. In this context, we have developed an automatic control method for indoor navigation. The proposed control system is mounted on the electric wheelchair for the handicapped, developed in the research laboratory CEMLab (Control and Energy Management Laboratory-Tunisia). The proposed method is based on two fuzzy controllers that ensure target achievement and obstacle avoidance. Furthermore, an extended Kalman filter was used to provide precise measurements and more effective data fusion localization. In this paper, we present the simulation and experimental results of the wheelchair navigation system.

Regression testing is a type of testing activity, which ensures that source code changes do not affect the unmodified portions of the software adversely. This testing activity may be very expensive in, some cases, due to the required time to execute the test suite. In order to execute the regression tests in a cost-effective manner, the optimization of regression test suite is crucial. This optimization can be achieved by applying test suite reduction (TSR), regression test selection (RTS), or test case prioritization (TCP) techniques. In this paper, we designed and implemented an expert system for TSR problem by using neuro-fuzzy modeling-based approaches known as “adaptive neuro-fuzzy inference system with grid partitioning” (ANFIS-GP) and “adaptive neuro-fuzzy inference system with subtractive clustering” (ANFIS-SC). Two case studies were performed to validate the model and fuzzy logic, multi-objective genetic algorithms (MOGAs), non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithms were used for benchmarking. The performance of the models were evaluated in terms of reduction of test suite size, reduction in fault detection rate, reduction in test suite execution time, and reduction in requirement coverage. The experimental results showed that our ANFIS-based optimization system is very effective to optimize the regression test suite and provides better performance than the other approaches evaluated in this study. Size and execution time of the test suite is reduced up to 50%, whereas loss in fault detection rate is between 0% and 25%.

Fuzzy logic-based inference systems depend on the domain experts’ perceptions, which are intrinsically imprecise/vague/fuzzy. The perceptions of more than one expert are needed in the decision-making process. Therefore, there is a need to study the similarity between the experts using a mathematical framework. Classical mathematical models simulating the medical diagnostic process are usually either logical or probabilistic, wherein the concept of partial belief is not considered. Except in a few cases, binary logic is too unrealistic to apply to medical diagnosis. Another important factor in medical science is the patient-symptom relationship, which influences the disease diagnosis. In summary, the following two issues stand out: (i) Do experts agree with one another in arriving at the same diagnostic labels? (ii) Based on the symptom-patient relationship, can patients be classified? The authors have tried to explore the possibility of using fuzzy similarity measures and also Gower’s coefficient in classifying gynaecologists and patients. The comparative evaluation infers that the efficacy of two-valued binary logic-based Gower’s coefficient is low.

In real life, a person may assume that an object belongs to a set, but it is possible that he (she) is not sure about it. In other words, there may be hesitation or confusion whether an object belongs to a set or not. In fuzzy set theory, there is no means to incorporate such type of hesitation or confusion. A possible solution is to use intuitionistic fuzzy set [K. T. Atanassov, Intutionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87–96]. In this article, the concept of unbalanced fully fuzzy multi-objective capacitated solid minimum cost flow (SMCF) problems is generalized by unbalanced intuitionistic fully fuzzy multi-objective capacitated SMCF (CSMCF) problems and new methods are proposed for solving these problems. The main advantage of the proposed methods over the existing methods is that all the unbalanced fully fuzzy single- and multi-objective CSMCF problems that can be solved by the existing methods can also be solved by the proposed method.

To find an optimal balance between accuracy and model transparency in fuzzy systems modeling, a novel approach based on the non-dominated sorting fireworks optimization algorithm (NSFOA) is proposed in this paper. The FOA is a new swarm intelligence algorithm mimicking the explosion of fireworks, which could be used to tune the parameters and optimize the structure of fuzzy systems with high effectiveness and correctness. At each iteration of the NSFOA algorithm, all individuals are sorted based on fast non-dominated sorting and crowding-distance evaluation, and the multiobjective fitness functions consider the aspects of both interpretability and accuracy contemporaneously. Subsequently, the individuals with better transparency and accuracy are selected for the next generation. The proposed NSFOA algorithm is applied to the second-order non-linear system and the Iris benchmark problem, and the experimental results demonstrate that our method leads to comprehensible fuzzy models with remarkable accuracy.

The issue of similarity measures of intuitionistic fuzzy sets (IFSs) is considered in this paper. Many existing similarity measures for two IFSs fail to take the abstention group influence into consideration and may lead to counterintuitive results in some cases. To deal with the problem, this paper first discusses the limitations of the existing similarity measures by some numerical examples, then, by considering the influence of abstention group, a new similarity measure of intuitionistic fuzzy sets is proposed, and the same numerical examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition, multicriteria group decision making, and medical diagnosis.

More serious chattering emerges in discrete systems of sliding mode control. The paper presents a sliding mode-like fuzzy logic control design, which eliminates the chattering, for a class of discrete nonlinear systems with multiple variables. First, the boundary layer is self-tuned on-line, and then, the chattering free is obtained. Consequently, the fuzzy logic control (FLC) is designed to approximate the sliding mode control (SMC) with boundary layer self-tuning. Finally, the performance of the robustness, chattering free, and adaption are verified by the simulation results.

We present some similarity and distance measures between intuitionistic fuzzy sets (IFSs). Thus, we propose two semi-metric distance measures between IFSs. The measures are applied to classification of shapes and handwritten Arabic sentences described with intuitionistic fuzzy information. The experimental results permitted to do a comparative analysis between intuitionistic fuzzy similarity and distance measures, which can facilitate the selection of such measure in similar applications.

In this paper, an improved technique for order preference by similarity to an ideal solution (TOPSIS) method was proposed based on completely unknown attribute weight information, as well as taking multiple criteria decision making of interval-valued intuitionistic fuzzy number as the evaluation information. First of all, a cumulative interval score function considering the influence of hesitation as well as a cumulative score function containing the risk preference of the decision maker were constructed. Then, a new information entropy function was constructed by using the newly defined score function, which presents a new method that directly utilizes evaluation information to obtain criterion weight. Next, all schemes were sequenced by virtue of relative closeness and the criterion weight of each alternative and ideal scheme. Finally, the effectiveness of the proposed method was illustrated by comparison with examples.

The studies of rough sets and soft sets, which can deal with uncertain problems in real life, have developed rapidly in recent years. We have known that linear space is a very important concept in linear algebra, so the aim of this paper was mainly focused on combining research in linear space, rough sets, and soft sets. First, according to the properties of upper (lower) approximation in rough linear space, the inclusion relation of the upper approximation’s union and the inclusion relation of the lower approximation’s intersection are improved. The equations of the upper approximation’s union and the lower approximation’s intersection are given. Secondly, the connection of linear space to rough sets is explored and the rough linear approximate space is proposed, which is proved to be a Boolean algebra under the intersection, union, and complementary operators. Thirdly, the combination of linear space and soft set is discussed, the definitions of soft linear space and soft linear subspace are proposed, and their properties are explored. Finally, the definitions of lower and upper approximation of a subspace X in soft linear space are given and their properties are studied. These investigations would enrich the studies of linear space, soft sets, and rough sets.

Fuzzy rule-based systems (FRBSs) are proficient in dealing with cognitive uncertainties like vagueness and ambiguity imperative to real-world decision-making situations. Fuzzy classification rules (FCRs) based on fuzzy logic provide a framework for a flexible human-like reasoning involving linguistic variables. Appropriate membership functions (MFs) and suitable number of linguistic terms – according to actual distribution of data – are useful to strengthen the knowledge base (rule base [RB]+ data base [DB]) of FRBSs. An RB is expected to be accurate and interpretable, and a DB must contain appropriate fuzzy constructs (type of MFs, number of linguistic terms, and positioning of parameters of MFs) for the success of any FRBS. Moreover, it would be fascinating to know how a system behaves in some rare/exceptional circumstances and what action ought to be taken in situations where generalized rules cease to work. In this article, we propose a three-phased approach for discovery of FCRs augmented with intra- and inter-class exceptions. A pre-processing algorithm is suggested to tune DB in terms of the MFs and number of linguistic terms for each attribute of a data set in the first phase. The second phase discovers FCRs employing a genetic algorithm approach. Subsequently, intra- and inter-class exceptions are incorporated in the rules in the third phase. The proposed approach is illustrated on an example data set and further validated on six UCI machine learning repository data sets. The results show that the approach has been able to discover more accurate, interpretable, and interesting rules. The rules with intra-class exceptions tell us about the unique objects of a category, and rules with inter-class exceptions enable us to take a right decision in the exceptional circumstances.

The very basis of the present article is the fact that the medical knowledge consisting of clinical presentation, diagnosis, and treatment of a disease is with imprecision and uncertainty. The overall approach in gynecological disease diagnosis could be divided into three distinct stages, and this was confirmed by seven experienced gynecologists. Stage 1 refers to an initial screening process in order to arrive at a single disease diagnosis for the patients, which is based only on the subjective information provided by patients to the physician. In stage 2, the patient who has not received a single diagnostic label in stage 1 is further investigated for a single disease diagnosis using past history criteria. If stage 2 fails to arrive at a single disease diagnosis for a patient, then physical examination and various tests like imaging tests, blood tests, etc., are conducted, and the test results are processed in stage 3. In stage 1, we have revisited fuzzy relational calculus and mathematically evaluated the perceptions of the domain experts (gynecologists) with respect to 31 gynecological diseases. The paper also presents the research findings with a case study focused on stage 2 using a type 1 fuzzy inference system. Out of 226 patients, 50 are correctly diagnosed for a single disease and 147 for multiple diseases in stage 1. The paper concludes that fuzzy relational calculus is an effective method as an “initial screening” process to arrive at a single disease diagnosis. We have identified 29 out of 226 patients satisfying past history criteria to achieve a single disease diagnosis by stage 2. Investigations for stage 3 are in progress.

Several applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of ( α , β )-fuzzy interior ideal. This new concept is called interval-valued (∈, ∈ ∨ qk˜)$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued (∈, ∈ ∨ qk˜)$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy ideals and interval-valued (∈, ∈ ∨ qk˜)$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued (∈, ∈ ∨ qk˜)$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals of an ordered semigroup is also an interval-valued (∈, ∈ ∨ qk˜)$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal.